Estimating the tracefree Ricci tensor in Ricci flow
Abstract
An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the tracefree Ricci tensor is controlled in a precise fashion by the other components of the irreducible decomposition of the curvature tensor, without any hypotheses on the initial data.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1153
 Bibcode:
 2007arXiv0711.1153K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 53C44 (Primary);
 53C21 (Secondary)